NEW YORK -- Dan Girardi tipped in a pass from defensive partner Ryan McDonagh to tie the game with 3:28 left in regulation and then returned the favor, setting up McDonagh's winner 1:56 into overtime to give New York a 4-3 victory against the Phoenix Coyotes on Monday night at Madison Square Garden.

Goalie Mike Smith stopped 25 of 27 shots before Thomas Greiss made seven saves in relief. Smith left the game because of a lower-body injury with 7:34 left in the third period.

"We'll see," Coyotes Head Coach Dave Tippett said of Smith's injury. "It's early. We don't know anything about it yet."

Despite the loss, Phoenix remains in possession of the Western Conference's second wild-card spot for the Stanley Cup Playoffs. The Coyotes sit one point ahead of the Dallas Stars, who defeated the Winnipeg Jets 2-1 on Monday and hold a game in hand.

Derick Brassard and Brad Richards also scored for the Rangers and Henrik Lundqvist made 18 saves.

Following a pre-game ceremony in which Lundqvist was honored for his recent 302nd career win and 50th NHL shutout, both franchise records, the Rangers came out sluggish. It didn't help that forwards Derek Stepan and Martin St. Louis were battling an illness that seemed to sap them of their energy.

"I made a mistake tonight. I shouldn't have played Step and Marty," Rangers coach Alain Vigneault said. "They didn't look good but they both said they wanted to play. At the end of the day, I've got to be better and I've got to take that out of their hands. They had no energy. Obviously it showed and I didn't play them much."

With St. Louis and Stepan limited, it was McDonagh who provided some offense when the Rangers needed it most. He won it for New York when he was left in front of the net and tapped in a rebound off Girardi's point shot past Greiss for his 13th.

The two connected on the equalizer late in the third, minutes after Smith was hurt with 7:34 remaining in regulation. The injury occurred when Brassard fell on him following a scramble in front. Smith appeared to be favoring his right leg and was helped to the dressing room.

Greiss made some big stops, but there was little he could do when Girardi tied the game 3-3 with 3:28 left in regulation. Down low at the tip of the crease, Girardi deflected in a McDonagh slap pass from the side of the net. Used to conservatively patrolling the blue line, it was an unlikely spot for Girardi to net his fifth.

"I didn't really know what to do. I just turned around and started screaming, looking for anybody to come at me," Girardi said. "I don't make it down there too often. It was nice to get one from down there."

New York's 3-2 deficit came off an unfortunate play by Chris Kreider that came just 30 seconds after the forward made a perfect pass to Stepan at the left wing for a quality scoring chance with 3:39 remaining in the second.

Chipchura sped down the left wing and centered a feed toward Antoine Vermette in the slot when Kreider stuck out his stick to break up the pass. But the rookie accidentally redirected the puck between Lundqvist's legs to give Chipchura his third of the season and Phoenix a 3-2 lead at 16:51.

The play sapped New York of some energy after an impressive second-period comeback.

Trailing 2-0, the Rangers finally solved Smith 6:10 into the second. Hagelin circled along the blue line before unleashing a rising wrister that Richards deflected low glove side for his 17th of the season and first in 11 games. The goal appeared to spark Richards, who stepped up in Stepan and St. Louis' absence, posting a plus-three rating and helping to set up McDonagh's winner with an aggressive forecheck.

Brassard tied the game at 10:53 after his cross-ice pass to St. Louis was blocked in close by Chris Summers. Staying with the puck, he snapped a shot from the right circle that beat an out-of-position Smith high for his 17th.

"I got a lucky bounce and the goalie cheated on the pass," Brassard said. "As soon as I saw he was out I just shot it as hard as I could."

It was a stark contrast to a first period in which Phoenix dominated.

Ekman-Larsson opened the scoring 4:40 into the game while Rick Nash served a tripping penalty. Keith Yandle made a perfect pass to hit Ekman-Larsson in stride down the right wing. The Swedish defenseman took a few strides before snapping a shot past Lundqvist for his 13th.

Halpern gave Phoenix a 2-0 lead at 8:22 after Chipchura found him streaking through the slot from behind the net. The former Ranger one-timed the feed low past Lundqvist for his fifth.

But as they've been prone to doing much of the season, Phoenix couldn't hold the lead.

"The thing we talked about after the first period is we know they're coming hard. You have to push back," Tippett said. "When we come out and turn pucks over and don't compete physically, it allows the other team to turn it."

Without their starting goaltender and forward Lauri Korpikoski, who missed the game after sustaining an upper-body injury in practice, the Coyotes must regroup in time to play against the Pittsburgh Penguins on Tuesday.

"We've got to get right back at it tomorrow," Tippett said. "There's no time to dwell on it."